Jake Faria became just the fifth pitcher since at least 1913 to win his first three starts in the majors with one or less runs in at least six innings.
Faria (3-0) joined Jeremy Hellickson as the only Tampa Bay pitcher to win his first three starts with a seven-inning outing in which he allowed six hits, walked one and struck out nine with his low-90s fastball and sharp-breaking slider.
Faria joined Andy Rincon (St. Louis, 1990), Wayne Simpson (Cincinnati, 1970), Stu Miller (St. Louis, 1952) and Alex Main (Detroit, 1914) as the only pitchers to win their first three major league starts allowing one or fewer runs while pitching at least six innings.
Chase Whitley pitched the eighth and Tommy Hunter the ninth for Tampa Bay.
Logan Morrison had two of the Rays' home runs to reach 21 for the season, a two-run blast to right in the first and a solo shot in the seventh.
Buck Farmer (2-1) served up two home runs in the third inning as the Rays jumped out to a 7-1 lead.
Derek Norris lined a flat 1-2 slider over the left-center field fence leading off the inning for his eighth home run.
Farmer gave up five hits and a walk plus a hit batter in 2 1/3 innings.
Corey Dickerson singled to left, Evan Longoria was hit by a pitch, Morrison walked and Souza Jr. hit a 2-2 slider over the fence in left center for his first career grand slam and 13th home run this season.
Justin Upton lined a single to center with two outs in the first for Detroit's first run. Alex Avila singled and Miguel Cabrera walked ahead of Upton's hit.
Morrison belted his 20th home run of the season with a man on in the first. Dickerson singled with one out and one out later Morrison lined a 1-2 pitch off the metal fencing atop the wall in right to stake the Rays to a 2-0 lead.
Longoria belted his 10th home run of the season with one out in the seventh off reliever Chad Bell and was followed on the next pitch by Morrison's second homer of the game.
NOTES: RHP Anibal Sanchez will be brought back from a voluntary minor league assignment Monday night to start for Detroit at Seattle. It's his first start of the season for the Tigers. ... Tampa Bay C Wilson Ramos (ACL surgery) didn't play Sunday after catching back-to-back games for the first time during his rehab stint. "We're getting closer," Rays manager Kevin Cash said. "We're getting excited." ... 2B Daniel Robertson is the first rookie Rays middle infielder to have at least two hits and two RBIs in consecutive games since Josh Wilson in 2007. Robertson did so Friday night and Saturday.